you have 160 yards of fencing to enclose a rectangular region. find the maximum area of the rectangular region

Answers

Answer 1

Answer:
I know that for a fixed perimeter, the shape that encloses the greatest area
is a circle, and the rectangle that encloses the greatest area is a square.
Sadly, I don't know how to prove it to you without Calculus.

If you'll take my assertion that the greatest rectangle is a square, and accept
it on faith, then you should use your 160-yd of fence to enclose a square with
40-yd sides. The area inside it is (40 x 40) = 1600 square yards.

Here are some other choices.
Each one has the same perimeter ... 160 yards.
This table kind of suggests to you that a square is the rectangle
   with the greatest area. (But it doesn't prove it.)

Length    Width    Area
35-yd     45-yd    1,575 square yards
30 50 1,500
25 55 1,375
20 60 1,200
15 65    975
10 70 700
    5 75    375
    3 77    231
    2 78    156
    1    79    79
2-ft 79-yd 1-ft    52.89
1-ft    79-yd 2-ft    26.56
1-inch 79-yd 35-in 2.19 square yards

With the same 160-yd of fence, you could have squeezed in some more
area by setting the fence down in a circle with circumference = 160-yd.
The area inside the circle would be

       Area = (pi) (radius)² = (circumference)² / (4 pi) = 2,037.2 square yards

The area of a circle is always (4 / pi) times the area of the square with the
same perimeter. That's about 27.3% more area than the square.

Answer 2

Answer: To optimize the area, the shape should be a square. Clearly, with 160 yards of fencing, the square will have side-length 160/4=40 yards. Therefore, the area will be 40*40=1600 yards.

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Would someone Please answer this question please will be thanked and also will pick brainly!! (please be honest)

Which points are solutions to the linear inequality; y < 0.5x + 2?

Answers

Answer:

A) $(-3,-2)$

C) $(-1,-2)$

E) $(1,-2)$

F) $(1,2)$

Step-by-step explanation:

we have

$y<0.5x+2$

The options are the points

$(-3,-2)$ , $(-2,1)$ , $(-1,-2)$ , $(-1,2)$ , $(1,-2)$ , $(1,2)$

we know that

If a ordered pair is a solution of the inequality

then

the ordered pair must be satisfy the inequality

Verify

Point A) $(-3,-2)$

Substitute the value of x and value of y in the inequality an compare

$-2<0.5(-3)+2$

$-2<0.5$ -------> is true

The ordered pair $(-3,-2)$ is a solution of the inequality

Point B) $(-2,1)$

Substitute the value of x and value of y in the inequality an compare

$1<0.5(-2)+2$

$1<1$ -------> is not true

The ordered pair $(-2,1)$ is not a solution of the inequality

Point C) $(-1,-2)$

Substitute the value of x and value of y in the inequality an compare

$-2<0.5(-1)+2$

$-2<1.5$ -------> is true

The ordered pair $(-1,-2)$ is a solution of the inequality

Point D) $(-1,2)$

Substitute the value of x and value of y in the inequality an compare

$2<0.5(-1)+2$

$2<1.5$ -------> is not true

The ordered pair $(-1,2)$ is not a solution of the inequality

Point E) $(1,-2)$

Substitute the value of x and value of y in the inequality an compare

$-2<0.5(1)+2$

$-2<2.5$ -------> is true

The ordered pair $(1,-2)$ is a solution of the inequality

Point F) $(1,2)$

Substitute the value of x and value of y in the inequality an compare

$2<0.5(1)+2$

$2<2.5$ -------> is true

The ordered pair $(1,2)$ is a solution of the inequality

Hi There

x= -4

y= 2

(-4,2)

I hope that's help !

How many different choices of a car does a person have a particular model comes in six colors and three styles

Answers

Answer:

Step-by-step explanation:

Each color has three styles and there is 6 colorsso eahc style has 6 colors to choose from. We simply multiply 6 with 3.

You get 18

Which sentence describes why polygon MNOP is congruent to polygon JKLP?

Answers

The segment MN is equal in size to the segment JK, the segment NO is equal in size to the segment KL, the segment OP is equal in size to the segment LP.

Monique collects data from a random sample of seventh graders in her school and finds that 8 out of 16 seventh graders participate in after-school activities. Write and solve a proportion to estimate the number of seventh graders n who participate in after-school activities if 136 seventh graders attend Monique's school. Write the proportion used to solve this problem. Choose the correct answer below.

Answers

Answer:

Whatever are you answer choices, choose 68 or the closest answer possible. (Can i have brainliest please?)

Step-by-step explanation:

8/16=x/136 would be the ratio because it is sample/population

Solving gets x=68 people.

Whatever are you answer choices, choose 68 or the closest answer possible.

In the two-column proof below, provide a reason for each statement.

Answers

The ∠4 (which is equal to ∠2) and ∠13 are congruent (∠4 ≅ ∠13) because they both form part of the angles that add up to 180 degrees. In the given conditions, we have ∠2 ≅ ∠1 (given), and ∠7 and ∠13 are supplementary angles.

Supplementary angles add up to 180 degrees, so we can conclude that ∠7 + ∠13 = 180 degrees.

Now, we can use the fact that ∠2 ≅ ∠1 to deduce that ∠2 = ∠1.

Since ∠7 and ∠13 add up to 180 degrees and ∠2 = ∠1, we can deduce that ∠2 + ∠13 = 180 degrees.

This means that ∠4 (which is equal to ∠2) and ∠13 are congruent (∠4 ≅ ∠13) because they both form part of the angles that add up to 180 degrees.

Learn more about angle:

brainly.com/question/29161034

#SPJ1

This question is not complete, Here I am attaching the complete question: Below i am attaching the image.

In the two-column proof below, provide a reason for each statement. Given: ∠ 2 ≅ ∠7 and ∠7 and ∠13 are supplementary angles Prove: ∠4 ≅ ∠13

Find the distance from the point (-3,6) to the line y=-3/2x-5

Answers

To find the distance from the point (-3,6) to the line y = -3/2x -5, we can use the formula for the distance between a point and a line. The formula is:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

In this case, A = -3/2, B = 1, and C = 5. Substituting these values into the formula and plugging in the coordinates of the point (-3,6), we get:

distance = |-3/2(-3) + 1(6) + 5| / sqrt((-3/2)^2 + 1^2)

Simplifying further, we get:

distance = |9/2 + 6 + 5| / sqrt(9/4 + 1)

Simplifying the fraction under the square root, we get:

distance = |9/2 + 6 + 5| / sqrt(9/4 + 4/4)

Continuing to simplify, we get:

distance = |9/2 + 6 + 5| / sqrt(13/4)

Calculating further, we get:

distance = |9/2 + 6 + 5| / sqrt(13)/2

Finally, simplifying and calculating, we get:

distance = |9/2 + 6 + 5| / sqrt(13)/2 = 20/ sqrt(13) ≈ 5.44 units

So, the distance from the point (-3,6) to the line y = -3/2x -5 is approximately 5.44 units.

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